Solving Data Sufficiency Questions Using Expert Tips

Table of Contents

This article is in continuation to our article on “How to solve data sufficiency questions?”. We recommend you go through it first. In this article, we will address solving data sufficiency questions using expert tips by looking at 5 different questions and apply our standard 3-steps process.

Before scrolling down to the respective solution section, solving these data sufficiency questions on your own can help boost your practice and confidence.

Practice Question 1: Option A

If x is a positive integer, what is the value of x?

(1) x^{3} = 27

(2) 4x + 3y = 15

Solution –

Step 1: Analyse Question Stem

x is a positive integer.

x > 0 and

x can be 1, 2, 3, 4…. and so on.

We need to find the value of x (or, say a unique value of x).

Here we are getting two different values of x. From statement 1 alone, we can’t get a unique value of x.

Hence, statement 1 is NOT sufficient, and we can eliminate answer options A and D.

Statement 2: 4x + 3y = 15, where x, and y are positive integers.

According to this statement, 4x + 3y = 15 and

X and y can be 1, 2, 3, 4, 5, …. and so on.

Now, 4x + 3y = 15

Or, , let us assume different values of y and see if we can get a unique value of x or not.

Case 1: If y = 1 then , this value of x is possible.

Case 2: If y = 2, then , x can’t be a fraction, so we can ignore this value of x.

Case 3: If y = 3, then , x can’t be a fraction, so we can ignore this value of x.

Case 4: If y =4, then , x can’t be a fraction, so we can ignore this value of x.

Case 5: If y = 5, then , x can’t be 0. So we can ignore this value of x.

If we further increase y, the resulting value of x will be negative, which is not possible as x is a positive integer.

Hence, we can see that, for the given conditions, the only possible value of x is 3.

Solution

As we can get a unique value of x, hence statement 2 is sufficient.

In this question, statement (1) alone is not sufficient, but statement (2) alone is sufficient.

Thus, the correct answer is Option B.

We further need not analyse the statements by combining them. As you can see, while analysing statement 2, our focus was solely on that particular statement and we put all our efforts in trying to get the answer from that statement only. This is a very important aspect, some students end up considering Statement 1 while analysing Statement 2 and that’s a completely incorrect approach.

Now, let’s look at a case where we actually need both statements to help us in solving data sufficiency questions.

Practice Question 3: Option C

If x is an integer, what is the value of x?

(1) x^{2} = 9

(2) 4x + 3y = 15, where x > 0

Solution

Step 1: Analyse Question Stem

x is an integer.

It means x can be -3, -2, -1, 0, 1, 2, 3, …and so on.

So, from statement 1 alone, we can’t get a unique value of x.

Hence, statement 1 is NOT sufficient and we can eliminate answer options A and D.

Statement 2: 4x + 3y = 15, where x > 0

According to this statement, 4x + 3y = 15 and x > 0

Also, x is an integer.

Now, 4x + 3y = 15 ⇒ ,

In the above equation, we know that x is a positive integer, however we don’t know the nature of y i.e. whether y is a positive integer, negative integer or fraction? So, let us consider following three cases:

Case 1: y is a positive integer,

Let’s say y = 1 then =3,

Case 2: y is a fraction.

Let’s say then

Case 3: y is a negative integer.

Let’s say y = -3 then

We can see that more than one values are possible for x.

Hence, statement 2 is also not sufficient and we can eliminate answer Option B.

Step 3: Analyse Statements by combining.

From statement 1: x = 3 or -3

From statement 2: x > 0 and it can be 2, 3, 6, etc.

On combining both the statements, we can see that only x = 3 is common in both the statements.

Thus, x = 3

Hence, BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.

Thus, the correct answer is Option C.

So, you can see, only when we don’t get a unique and definite answer from any statement, then ONLY we combine both the statements to get the answer.

Practice Question 4: Option D

If x is a positive integer, what is the value of x?

So, from statement 1 alone, we can’t get a unique value of x.

Hence, statement 1 is not sufficient and we can eliminate answer Options A and D.

Statement 2: 4x + 3y = 15

According to this statement, 4x + 3y = 15

Or,

Here, we have 2 variables i.e. x and y and only one equation.

No additional information about the nature of y is given i.e. whether y is a positive integer, negative integer or it is a fraction.

So, let us consider one simple possibility that y is a positive integer. Thus, we will get many cases as y can be 1, 2, 3, 4… and so on. For example:

Case 1: Let’s say y = 1, then , this is possible

Case 2: Let’s say y = 4, then , this is not possible as x cannot be a fraction.

Case 3: Let’s say y = 9, then this is possible.

From the above cases we can see that we are getting different values of x i.e. x can be -3, 3, etc.

Hence, statement 2 is also NOT sufficient and we can eliminate answer B.

Step 3: Analyse Statements by combining.

From statement 1: x = -3 or 3

From statement 2: x can be 3, -3 etc.

On combining both the statements, we get, x = -3 or 3

We can observe that even after combining the two statements, we are not getting a unique value of x.

Hence, Statement (1) and (2) TOGETHER are NOT sufficient.

Thus, the correct answer is Option E.

The Conclusion

In this article, we focused on how we get an answer as A, B, C, D, or E while solving data sufficiency type questions. We solved 5 practice questions and learned how to apply the standard 3-steps process to solve DS questions and get the correct answer. You are recommended to solve more DS questions to perfectly understand this 3-step process.

Further, if you have noticed, in all 5 practice questions, you were asked to find a unique value of x. This is one type of DS question which you will get in the GMAT. However, there is one more type of DS question. That’s why, to make you more familiar with DS questions and help you to master the art of solving data sufficiency questions, in our next article, we will discuss two types of DS questions and two common mistakes made by students. So, do read the next article.

Table of Contents

This article is in continuation to our article on “How to solve data sufficiency questions?”. We recommend you go through it first. In this article, we will address solving data sufficiency questions using expert tips by looking at 5 different questions and apply our standard 3-steps process.

Before scrolling down to the respective solution section, solving these data sufficiency questions on your own can help boost your practice and confidence.

## Practice Question 1: Option A

If x is a positive integer, what is the value of x?

(1) x

^{3}= 27(2) 4x + 3y = 15

## Solution –

## Step 1: Analyse Question Stem

We need to find the value of x (or, say a

uniquevalue of x).## Step 2: Analyse Statements Independently (And eliminate options) – AD/BCE

Statement 1:x^{3}= 27x^{3}= 27So, from statement 1 alone we can find the

uniquevalue of x. Hence, statement 1 is sufficient and we can eliminate answer options B, C and E.Statement 2:4x + 3y = 154x + 3y = 15Hence, statement 2 is NOT sufficient.

In this question,

statement (1) alone is sufficient, but statement (2) alone is not sufficient.Thus, the correct answer is

OptionA.We further need not analyze the statements by combining them.

So, I hope, it’s clear, how we can get Option A as the answer while solving data sufficiency questions. Now, let’s move to the next question.

## Practice Question 2: Option B

If x is an integer, what is the value of x?

(1) x

^{2}= 9(2) 4x + 3y = 15, where x, and y are positive integers

## Solution

## Step 1: Analyse Question Stem

We need to find a

uniquevalue of x.## Step 2: Analyse Statements Independently (And eliminate options) – AD/BCE

Statement 1:x2 = 9Here we are getting two different values of x. From statement 1 alone, we can’t get a unique value of x.

Hence, statement 1 is NOT sufficient, and we can eliminate answer options A and D.

Statement 2:4x + 3y = 15, where x, and y are positive integers.## Solution

As we can get a unique value of x, hence statement 2 is sufficient.

In this question,

statement (1) alone is not sufficient, but statement (2) alone is sufficient.Thus, the correct answer is

Option B.We further need not analyse the statements by combining them. As you can see, while analysing statement 2, our focus was solely on that particular statement and we put all our efforts in trying to get the answer from that statement only. This is a very important aspect, some students end up considering Statement 1 while analysing Statement 2 and that’s a completely incorrect approach.

Now, let’s look at a case where we actually need both statements to help us in solving data sufficiency questions.

## Practice Question 3: Option C

If x is an integer, what is the value of x?

(1) x

^{2}= 9(2) 4x + 3y = 15, where x > 0

## Solution

## Step 1: Analyse Question Stem

We need to find a

uniquevalue of x.## Step 2: Analyse Statements Independently (And eliminate options) – AD/BCE

Statement 1:x^{2}= 9So, from statement 1 alone, we can’t get a unique value of x.

Hence, statement 1 is NOT sufficient and we can eliminate answer options A and D.

Statement 2:4x + 3y = 15, where x > 0Hence, statement 2 is also not sufficient and we can eliminate answer Option B.

## Step 3: Analyse Statements by combining.

Hence,

BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.Thus, the correct answer is

.Option CSo, you can see, only when we don’t get a unique and definite answer from any statement, then ONLY we combine both the statements to get the answer.

## Practice Question 4: Option D

If x is a positive integer, what is the value of x?

(1) x

^{3}= 27(2) 4x + 3y = 15, where y is a positive integer

## Solution

## Step 1: Analyse Question Stem

We need to find a

uniquevalue of x.Let’s move to the next step.

## Step 2: Analyse Statements Independently (And eliminate options) – AD/BCE

Statement 1:So, from statement 1 alone we can find a

uniquevalue of x.Hence, statement 1 is sufficient and we can eliminate answer Options B, C and E

Statement 2:4x + 3y = 15, where y is a positive integerHence, statement 2 is also sufficient.

So,

EACH statement ALONE is sufficient.Thus, the correct answer is

Option D.Now, let’s come to the final question!!

## Practice Question 5: Option E

If x is an integer, what is the value of x?

(1) x

^{2}= 9(2) 4x + 3y = 15

## Solution

## Step 1: Analyse Question Stem

We need to find the

uniquevalue of x.## Step 2: Analyse Statements Independently (And eliminate options) – AD/BCE

Statement 1:So, from statement 1 alone, we can’t get a unique value of x.

Hence, statement 1 is not sufficient and we can eliminate answer Options A and D.

Statement 2:4x + 3y = 15Hence, statement 2 is also NOT sufficient and we can eliminate answer B.

## Step 3: Analyse Statements by combining.

We can observe that even after combining the two statements, we are not getting a unique value of x.

Hence,

Statement (1) and (2) TOGETHER are NOT sufficient.Thus, the correct answer is

Option E.## The Conclusion

In this article, we focused on how we get an answer as A, B, C, D, or E while solving data sufficiency type questions. We solved 5 practice questions and learned how to apply the standard 3-steps process to solve DS questions and get the correct answer. You are recommended to solve more DS questions to perfectly understand this 3-step process.

Further, if you have noticed, in all 5 practice questions, you were asked to find a unique value of x. This is one type of DS question which you will get in the GMAT. However, there is one more type of DS question. That’s why, to make you more familiar with DS questions and help you to master the art of solving data sufficiency questions, in our next article, we will discuss two types of DS questions and two common mistakes made by students. So, do read the next article.

5 most common mistakes and how to avoid themSuggested Read:## Related posts:

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